Chebyshev Polynomials in Numerical Analysis by L Fox, I B Parker

By L Fox, I B Parker

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Learning and relearning in Boltzmann machines. In D. E. Rumelhart & J. L. , Parallel distributed processing: Volume 1, 282-317. Cambridge, MA: MIT Press. Hogan, N. 1984. An organising principle for a class of voluntary movements. Journal of Neuroscience, 4, 2745-2754. 61 Hollerbach, J. M. 1982. Computers, brains, and the control of movement. Trends in Neuroscience, 5, 189-193. Jordan, M. , & Rosenbaum, D. A. 1989. Action. In M. I. , Foundations of Cognitive Science. Cambridge, MA: MIT Press.

Let us represent the features of the input pattern by a set of real numbers x1; x2 ; : : : ; xn . For each input value xi there is a corresponding weight wi . The perceptron sums up the weighted feature values and compares the weighted sum to a threshold . If the sum is greater than the threshold, the output is one, otherwise the output is zero. That is, the binary output y is computed as follows:  1 if w1x1 + w2x2 +    + wnxn y= 24 0 otherwise 31 -1 x1 x2 x2 θ w1 w2 w1 x1 + w2 x 2 > θ y wn w1 x1 + w2 x 2 < θ xn x1 (a) (b) Figure 14: a A perceptron.

11 It has been suggested Miall, Weir, Wolpert, & Stein, in press that the distal supervised learning approach requires using the backpropagation algorithm of Rumelhart, Hinton, and Williams 1986. This is not the case; indeed, a wide variety of supervised learning algorithms are applicable. The only requirement of the algorithm is that it obey an architectural 11 50 D + Plant y [n ] _ ^x [n ] D y*[n +1] Feedforward Controller u[n ] D Forward Model y^ [n ] _ + Figure 26: The distal supervised learning approach.

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